Lattice study of trapped fermions at unitarity

TL;DR

This paper reports a lattice simulation of up to 20 unitary fermions in a harmonic trap, achieving high accuracy for small N and enabling predictions for larger N beyond traditional computational methods, with potential applications in nuclear physics.

Contribution

It introduces a lattice approach to study trapped unitary fermions, improving accuracy for small systems and extending the analysis to larger systems inaccessible by previous methods.

Findings

Achieved better than 1% agreement with exact solutions for N=6 fermions.

Extended the study to N=20 fermions, surpassing previous computational limits.

Highlighted potential for applying these methods to nuclear physics simulations.

Abstract

We present a lattice study of up to N=20 unitary fermions confined to a harmonic trap. Our preliminary results show better than 1% agreement with high precision solutions to the many-body Schrodinger equation for up to N=6. We are able to make predictions for larger N which were inaccessible by the Hamiltonian approach due to computational limitations. Harmonic traps are used experimentally to study cold atoms tuned to a Feshbach resonance. We show that they also provide certain benefits to numerical studies of many-body correlators on the lattice. In particular, we anticipate that the methods described here could be used for studying nuclear physics.